Optimization Using Indirect Design Coding

ABSTRACT

A method for optimizing a material structure. The method comprises the steps of encoding an initial design of the material structure to be optimized as a parameter set, subjecting the initial design to an optimization according to at least one preset criterion, using an evolutionary algorithm, terminating the optimization when a termination condition is met, and outputting data representing the optimized parameter set. The design of the material structure is encoded indirectly as a virtual DNA.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(a) to EuropeanPatent Application number 07 105 378, filed on Mar. 30, 2007, andEuropean Patent Application number 07 106 515, filed on Apr. 19, 2007,which are incorporated by reference herein in their entirety.

FIELD OF THE INVENTION

The present invention is related to optimization of physical bodies,more specifically to optimization of an internal structure of physicalbodies.

BACKGROUND OF THE INVENTION

Evolutionary algorithms have been successfully employed in variousfields including, among others, technical optimization, operationsresearch, and design optimization. In particular, innovative technicaldesign solutions were obtained in the field of design optimization byusing evolutionary algorithms in combination with appropriate simulationtools such as computational fluid dynamics.

The complexity of the design, however, is limited when using theevolutionary algorithms because in most cases (for example, splinerepresentation), the complexity is governed by the dimension of thesearch space. Alternative representations such as free form deformationallow shapes of unrestricted complexity to be designed. The free formdeformation, however, does not allow unrestricted changes in the shape.Further, it is also difficult to constrain the design to shapes andstructures with certain properties that may be desirable in some cases(for example, symmetry, self-similarity or properties that reflectconstraints of the physical world).

SUMMARY OF THE INVENTION

Embodiments of the present invention provide an improved designoptimization approach particularly adapted for optimization of the innerstructures of physical bodies.

In one embodiment of the present invention, a method for optimizing theinternal structure of a body includes: (a) encoding an initial design ofthe internal structure to be optimized as a parameter set; (b)subjecting the parameter set of the initial design to an optimizationaccording to at least one preset criterion using an EvolutionaryAlgorithm; (c) terminating the optimization when a termination conditionis met; and (d) outputting data representing the optimized parameterset. The design of the internal structure is encoded indirectly as avirtual genotype. The parameters of the virtual genotype describe a cellgrowth development of the phenotype in a gene regulatory network.Therefore, the virtual genotype represents an indirect coding of theinternal structure, for example, by the interaction behavior in the generegulatory network.

In one embodiment of the present invention, the internal structurecomprises voids.

In one embodiment of the present invention, the step of (e) building thebody having the internal structure of the optimized parameter set isalso performed.

In one embodiment of the present invention, the internal structure is atwo dimensional cross-section of the body or a three-dimensionalinternal structure of the body.

In one embodiment of the present invention, the step (b) of subjectingthe parameter set of the initial design to an optimization includesrepeating the following steps: (i) producing offspring of a genotype,(ii) developing cell growth until a development termination criterion ismet (the development is directed by the genotype, leading to thephenotype of the offspring individuals), (iii) computing a fitness valueof the grown phenotype, and (iv) selecting the individuals according totheir fitness value and a selection strategy (for example, highestfitness value) for the subsequent offspring production step.

In one embodiment of the present invention, the step of producingoffspring from a parent individual is at least one of (i) mutation ofthe genotype, (ii) crossover with another individual, (iii) genetransposition, and (iv) gene duplication. Therefore, the production ofoffspring individuals occurs at the genotype level and not at thephenotype level.

A development termination condition is met, for example, when (i) thecell growth development reaches a predetermined number of discrete stepsor (ii) the cell growth development converges into a stable structure(i.e., the change in the cell growth development between two subsequentsteps is lower than a predetermined threshold).

In one embodiment of the present invention, the cells represent thepresence of material or holes at a defined position.

In one embodiment of the present invention, the cells representdifferent materials. For example, the material type can be encoded inthe genotype of an individual, and thereby be differentiated indifferent cells of an individual.

In one embodiment of the present invention, after terminating the cellgrowth development, the phenotype of the internal structure can besmoothened. The cells represent control points of a higher order splinesurface or other smoothing methods.

In one embodiment of the present invention, the material boundary ofmaterials of different type or holes is represented by patches from anumber of different spline surfaces.

In one embodiment of the present invention, the cells move according tothe forces applied by other cells or the environment during the cellgrowth development.

In one embodiment of the present invention, the cells may interactphysically in the form of rigid body interaction during the cell growthdevelopment.

In one embodiment of the present invention, the cells may be pushedaside when a division occurs and may reach a new stable arrangementafterwards during the cell growth development.

In one embodiment of the present invention, the number of parameters ofthe genotype varies during the course of the optimization. That is,adaptive number of parameters is allowed.

In one embodiment of the present invention, the parameters of thegenotype define the activity and the action type of a cell during thecell growth development.

In one embodiment of the present invention, the activity is at least oneof divide, die, release transcription factor (TF) and produce a celladhesion function.

In one embodiment of the present invention, the activity is the cellassuming one out of a plurality of different material types allowed foroptimization of the body.

In one embodiment of the present invention, the Evolutionary Algorithmis an Evolution Strategy.

The features and advantages described in the specification are not allinclusive and, in particular, many additional features and advantageswill be apparent to one of ordinary skill in the art in view of thedrawings, specification, and claims. Moreover, it should be noted thatthe language used in the specification has been principally selected forreadability and instructional purposes, and may not have been selectedto delineate or circumscribe the inventive subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The teachings of the present invention can be readily understood byconsidering the following detailed description in conjunction with theaccompanying drawings.

FIG. 1 is a diagram illustrating a vDNA, according to one embodiment ofthe present invention.

FIG. 2 is a diagram illustrating a gene regulatory network, according toone embodiment of the present invention.

FIG. 3 is a series of diagrams illustrating interactions inside thedynamic gene regulatory network, according to one embodiment of thepresent invention.

FIG. 4 is a diagram illustrating an example of developing the fitness asa function of the optimization cycle (generation) number, according toone embodiment of the present invention.

FIG. 5 is a flow chart illustrating a method, according to oneembodiment of the present invention.

FIG. 6 is a diagram illustrating different stages of the cell growthdevelopment of a phenotype, according to one embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

A preferred embodiment of the present invention is now described withreference to the figures where like reference numbers indicate identicalor functionally similar elements.

Reference in the specification to “one embodiment” or to “an embodiment”means that a particular feature, structure, or characteristic describedin connection with the embodiments is included in at least oneembodiment of the invention. The appearances of the phrase “in oneembodiment” in various places in the specification are not necessarilyall referring to the same embodiment.

Some portions of the detailed description that follows are presented interms of algorithms and symbolic representations of operations on databits within a computer memory. These algorithmic descriptions andrepresentations are the means used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. An algorithm is here, and generally,conceived to be a self-consistent sequence of steps (instructions)leading to a desired result. The steps are those requiring physicalmanipulations of physical quantities. Usually, though not necessarily,these quantities take the form of electrical, magnetic or opticalsignals capable of being stored, transferred, combined, compared andotherwise manipulated. It is convenient at times, principally forreasons of common usage, to refer to these signals as bits, values,elements, symbols, characters, terms, numbers, or the like. Furthermore,it is also convenient at times, to refer to certain arrangements ofsteps requiring physical manipulations of physical quantities as modulesor code devices, without loss of generality.

However, all of these and similar terms are to be associated with theappropriate physical quantities and are merely convenient labels appliedto these quantities. Unless specifically stated otherwise as apparentfrom the following discussion, it is appreciated that throughout thedescription, discussions utilizing terms such as “processing” or“computing” or “calculating” or “determining” or “displaying” or“determining” or the like, refer to the action and processes of acomputer system, or similar electronic computing device, thatmanipulates and transforms data represented as physical (electronic)quantities within the computer system memories or registers or othersuch information storage, transmission or display devices.

Certain aspects of the present invention include process steps andinstructions described herein in the form of an algorithm. It should benoted that the process steps and instructions of the present inventioncould be embodied in software, firmware or hardware, and when embodiedin software, could be downloaded to reside on and be operated fromdifferent platforms used by a variety of operating systems.

The present invention also relates to an apparatus for performing theoperations herein. This apparatus may be specially constructed for therequired purposes, or it may comprise a general-purpose computerselectively activated or reconfigured by a computer program stored inthe computer. Such a computer program may be stored in a computerreadable storage medium, such as, but is not limited to, any type ofdisk including floppy disks, optical disks, CD-ROMs, magnetic-opticaldisks, read-only memories (ROMs), random access memories (RAMs), EPROMs,EEPROMs, magnetic or optical cards, application specific integratedcircuits (ASICs), or any type of media suitable for storing electronicinstructions, and each coupled to a computer system bus. Furthermore,the computers referred to in the specification may include a singleprocessor or may be architectures employing multiple processor designsfor increased computing capability.

The algorithms and displays presented herein are not inherently relatedto any particular computer or other apparatus. Various general-purposesystems may also be used with programs in accordance with the teachingsherein, or it may prove convenient to construct more specializedapparatus to perform the required method steps. The required structurefor a variety of these systems will appear from the description below.In addition, the present invention is not described with reference toany particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof the present invention as described herein, and any references belowto specific languages are provided for disclosure of enablement and bestmode of the present invention.

In addition, the language used in the specification has been principallyselected for readability and instructional purposes, and may not havebeen selected to delineate or circumscribe the inventive subject matter.Accordingly, the disclosure of the present invention is intended to beillustrative, but not limiting, of the scope of the invention, which isset forth in the following claims. Effectors include manipulators inindustrial robots. In humanoid robotics, the effector is often definedas a reference point of the hand such as the finger tip. The effectorcould also be the head, which is controlled to face a certain point orin certain direction.

In one or more embodiments of the present invention, a parameter setrepresenting an optimized design of a physical body is obtained. Thisoptimized parameter set may then be translated into a real worldphysical body. The optimization may be carried out using a conventionalEvolutionary Algorithm that is well known to a person skilled in theart.

With reference to FIG. 5, a general layout of the method according tothe present invention is described below.

It is an object of this method to generate data representing thestructure of an optimized physical body. The “optimized physical body”is to be understood as a physical body that is optimized in cycliciterative steps in view of one or a plurality of (multiple) objectives.

In the first step, a population of individuals is defined. Eachindividual contains a virtual DNA (vDNA) as genotype. The vDNA is thebasis for the gene regulatory network (GRN) that controls the growthprocess of the individuals. In order to define a GRN, the input andoutput behavior of virtual cells and the interaction mechanisms betweenthe cells need to be defined.

In a second step, a population of initial non-optimized designs isindirectly encoded as the vDNA of the individuals. The vDNA comprises aplurality of genes (see FIG. 1), each consisting of, for example, aplurality of structural subunits (SU) and regulatory subunits (RU).Thus, input behavior, output behavior and the interaction between thecells are encoded via the genes of the vDNA. This encoding is called“indirect encoding” as the parameters (values inside the genes) of thevDNA do not directly encode the shape of an individual (for example, viathe coordinates of splines, the angles of flaps of a wing, etc.) butrather provides a construction plan using which the shape is grown. Theencoding is indirect because in order to develop the phenotype, a cellwith such vDNA must first undergo a cell growth development process toproduce the phenotype.

The initial genome of the vDNA may, for example, be set up by randomlyallocating values to all subunits of the genes of the virtual DNA. Analternative is to set all values on an average value or use a hand codedgenotype as well as a genotype that proved useful during previousevolutionary runs.

It is well known in evolutionary algorithms that several offspringindividuals are then produced from this initial population ofindividuals referred to as parent population. It is also well known thatthe several offspring individuals will differ slightly from each other(and from the initial parent individuals) because the offspringproduction process usually comprises some random influence such asmutation. Thus, this offspring generation will have at least twoindividuals with usually slightly different vDNAs.

Note that in the case of the direct encoding (for example, splineencoding) of known evolutionary algorithms, the direct encoding of theindividuals may be mapped directly to phenotype designs. The fitness ofthese differing phenotypes may be assessed or computed by applying afitness function.

In contrast, in view of the indirect encoding of the present invention,the individuals of the offspring population have to be developed (cellgrowth development) using a gene regulatory network in order to producediffering phenotypes. The cell growth development is terminated when adevelopment termination condition is met. The development terminationcondition, for example, is reaching of a preset number of developmentalsteps or stabilization of the cell growth development process (i.e., thedifference between two subsequent steps is smaller than a presetdevelopment change threshold). At the end of the cell growth developmentstep, each individual of the population grows a phenotype that generallydiffers from the phenotypes of other individuals.

Then, a fitness function (well known in evolutionary algorithms) may beapplied to the differing phenotypes to assess the fitness in view of atleast one preset optimization criterion. The fitness function outputs acomputed fitness value for each of the offspring phenotypes.

If the termination criterion for the optimization cycle is not reached,individuals of this offspring population are subject to selection.According to the fitness values and a selection strategy, a subset ofindividuals is chosen to serve as new parent population for subsequentiterations of the optimization loop.

In one embodiment, the fitness assessment and the selection are madeusing an assessment on the phenotypes. The offspring generation(including mutation) is carried out at the vDNA level. This is differentfrom conventional evolutionary algorithms in which the genotype and thephenotype are directly linked and a change in phenotype yields adirectly predictable change in the phenotype.

If an optimization termination condition is met after the fitnessassessment, the optimization cycle terminates. The optimizationtermination condition can be, for example, (i) reaching of a presetmaximum number of optimization cycles, (ii) satisfying a convergencecriterion (i.e., the fact that the fitness value of the best phenotypesof subsequent optimization cycles shows a difference which is smallerthan a preset convergence threshold) or (iii) reaching of a requiredfitness value.

When the optimization cycle is terminated, data representing theoptimized phenotype or the vDNA of the optimized phenotype can beoutputted.

These data can then be used as a two-dimensional cross section orthree-dimensional representation of the corresponding physical body tobe built.

In one or more embodiments of the present invention, the modeling ofcellular development is conducted by Gene Regulatory Networks (GRNs) forevolutionary shape or structure optimization.

In one or more embodiments of the present invention, the developmentalprocess that uses cells as phenotypic representation is used for designoptimization. The genotype of an individual represents a vDNA. Theindividual is subject to the process of evolution using an EvolutionaryAlgorithm. The genotype (vDNA) describes the developmental process of agrowing phenotype rather than its final appearance. Generally,individuals grow in discrete steps (developmental time steps) from onecell to the final shape using simulated physical and chemical cell-cellinteractions such as simulated transcription factors and simulatedadhesion forces between cells.

Environment

The optimization process starts from the definition of an environment(“virtual egg”) that provides the physical environment for thesimulation of development. The environment is in the form of a cube (x,y and z directions) with fixed boundaries. At the beginning of thedevelopment, a virtual egg contains one single cell in the shape of aball of a fixed radius at the center of the cube. Generally, cellpositions are determined by floating point values for x, y and z, andare in general affected by the forces exerted by other cells. Therefore,the cells may move during the developmental process.

Cell

Cells are entities that represent the phenotype because positions of thecells are evaluated for fitness computation. All cells inside onevirtual egg contain the same vDNA. The cells are capable of dividing,which means that a new cell is placed close to the first cell. The exactposition of the new cell depends on genetic information and the positionand forces of other cells.

The cells are capable of producing a number of transcription factorsthat diffuse inside the egg. After apoptosis (i.e., genetically inducedcell death), the cell is removed from the virtual egg.

Virtual DNA (vDNA)

The virtual DNA is a vector of genes. Each gene consists of a randomnumber of structural units (SU) and several regulatory units (RU). Thestructural units provide information for the cell's actions. Theregulatory units act as controlling entities. The activation function ofthe regulatory units is evaluated in every developmental time step.Specifically, depending on the presence of transcription factors, allregulatory units of one gene contribute to its overall activity. Thatis, they determine whether a gene is active or inactive at the positionwhere the cell is located.

Transcription Factors

Transcription factors (TFs) are simulated chemicals that consist of atype aTF, a distribution of concentrations that is associated with everypoint of a diffusion grid d, a diffusion constant D, and a decay rate g.The type is used to compute a chemical distance to the regulatory units.Therefore, a transcription factor with a small chemical distance to aregulatory unit has a greater influence on that unit than TFs withlarger distances. This ensures that regulatory units will reactspecifically to certain TFs as described below in detail.

Evolutionary optimization in a developmental process according toembodiments of the present invention combines evolutionary computationwith cell growth development. In this approach, an artificial genotypeencodes the developmental process through Gene Regulatory Networks(GRNs) resulting in an indirect representation that is different fromtraditional evolutionary algorithms (EAs).

Process of Development

The model according to embodiments of the present invention is based onextensions of the model disclosed, for example, in T. Steiner, M.Olhofer, and B. Sendhoff, “Towards shape and structure optimization withevolutionary development,” In Proceedings of the Tenth InternationalConference on the Simulation and Synthesis of Living Systems, pages70-76, 2006, which is incorporated by reference herein in its entirety.There are two major extensions from the method disclosed in thisarticle: (i) implementation of physical interactions between cells, and(ii) modifications to the genetic representation so that the modelbecomes biologically more plausible.

Genetics

According to the embodiments of the present invention, cellular growthis controlled by a genome stored in a virtual DNA (vDNA). An identicalcopy of the vDNA is available for translation to all cells in anindividual.

This genome consists of regulatory subunits (RUs) and structuralsubunits (SUs), which are initially lined up in a random order. Thefunctional unit of this DNA, called a gene, is composed of a group ofSUs and the preceding RUs. The SUs encode actions that a cell shouldperform while the RUs determine whether a gene is active or not. Theactions encoded in the gene will be performed only if the gene isactive.

An illustrative example of a genome with three genes is shown in FIG. 1.This Figure shows a vDNA with three genes, each consisting of one ormore structural subunits (SUs) and regulatory subunits (RUs). Twodifferent types of RUs exist: (i) inhibitor (RU−), and (ii) activator(RU+). A SU coding for the production of a transcription factor (TF) isdenoted by SUTF, a SU coding for a division by SUdiv and a Cadherinproducing SU by SUcad.

Structural subunits: A SU encodes the action to be performed, andcontains the parameters that specify the action. Possible actionsinclude cell division, production of a diffusing chemical, thetranscription factor (TF) for cell-cell signaling, and production ofCadherin molecules on the cell surface, which determine cell-celladhesion forces.

Formally, a SU consists of a five element vector x with entries x_(i)ε[0. . . 1], i=1, . . . , 5. x₁ is used to determine the type t of actionencoded by the SU:

$t = \left\{ \begin{matrix}1 & {\forall{x\text{:}}} & {0\; \leq x_{1} < \frac{1}{3}} \\2 & {\forall{x\text{:}}} & {\frac{1}{3} \leq x_{1} < \frac{2}{3}} \\3 & {\forall{x\text{:}}} & {\frac{2}{3} \leq x_{1} < 1}\end{matrix} \right.$

If t=1, a cell division is encoded. x₂ is used to determine the divisionangle while the values x₃ to x₅ remain unused. If t=2, a TF is to beproduced. x₂ encodes an affinity label assigned to the TF (aff_(TF)), x₃is the amount of TF to be released, x₄ is a diffusion constant, and x₅is a decay rate. In case where t=3, Cadherin molecules are to beproduced by the gene, and the type of Cadherin is determined by x₂.

Cells containing the same type of Cadherin will adhere to each other.Note that for t=2, not all x_(i) are used but they are still kept as apart of the SU. This means that mutation affects them but they are notsubject to selection pressure. The reason for keeping all x_(i) is thata mutation in x₁ can yield t=2, where five values are needed for theproduction of the TF. Comparison of this pragmatic to otherpossibilities were not yet explored (for example, to a randomre-initialization of x₂ to x₅ when x₁ causes a change in t).

Regulatory subunits: Two types of RUs are used in the model, whicheither increase (activate) or decrease (inhibit) the expression of agene. The RUs can sense the presence of certain types of TFs in thevicinity of the cell. If the label of a TF is affine to a labelassociated with the RU and the concentration of the TF lies above athreshold, an activity value is determined for each RU. All activating(=positive sign) and inhibiting (=negative sign) activity valuesbelonging to the same gene are summed up to determine the overallactivity of the gene.

Cells and their Interaction

The simulation area for cellular growth is defined by a square (2D) or acube (3D) that is discretized by an equally spaced grid (for example,step-size=0.5) on which the concentrations of the TFs are allocated. Thecells are modeled, for example, as spheres having a radius of one. Thecells interact with each other by reading and releasing TFs and bycellular motion through rigid body interactions coupled with adhesionforces.

No deformation to the spheres is allowed. Instead, a small overlapbetween neighboring cells is allowed. Note that the cell positions arenot fixed to a grid. Therefore, they read the concentrations of TFs fromthe four nearest nodes of the diffusion grid and interpolate its actualvalue. The release of a TF by a cell is simulated by an increase ofconcentration in the four nearest nodes on the diffusion grid.

In one embodiment of the present invention, the implemented mechanismfor cell adhesion is as follows: If two cells contain the same type ofCadherins (which means that they express the same gene), the cells willadhere to each other.

There are several alternative models available for the simulation ofcellular growth and their interaction. For example, the cells may bemodeled as pixels on a fixed grid. A spring mass-damper system isemployed to simulate the shape and physical behavior of plant cells. Asdescribed above, different cell models require the evolution ofdifferent control mechanisms, resulting in different gene regulatorysystems with varying properties.

In one embodiment of the present invention, a cell can always performthe actions that its genome activates. In contrast, it may be the casethat a division does not take place in the pixel model because the spacefor the new cell is already occupied by another cell. Therefore, thecontrol of activation for such a gene would no longer evolve because itsfunction is automatically disabled.

Time Scales and Sequence of Events

At the beginning of the development, a single cell containing the vDNAis placed at the center of the simulation area. To start the growthprocess, an initial TF (maternal TF) is released, which maintains aconstant concentration in the whole area over the entire developmentaltime. Contrary to most existing models, the initial TF concentration inthe embodiments of the present invention does not provide any positionalinformation. Rather, it satisfies the minimal requirement for starting adevelopmental process.

In each developmental step, the following events take place: First, thetranslation of the DNA is initialized for all existing cells. Secondly,if the TFs in the vicinity of the cell activate a gene, the actionencoded in the gene is executed. Finally, the position of all cells isupdated and the diffusion of the released chemicals is simulated.

FIG. 2 illustrates the static interaction network of an individual fromgeneration 43, according to one embodiment of the present invention. Theprediffused TF is placed at the center of the network. A close-up on onegene is shown in the upper left corner of the Figure. The gene consistsof an inhibitory RU (black ellipses), an excitatory RU (white ellipses)and two TF-coding Sus (rectangles). Two interacting genes and theprediffused TF are emphasized by bold circles.

FIG. 3 illustrates a series of interactions inside the dynamic GRN,according to one embodiment of the present invention. Each gene is shownas a small circle. The point denotes the prediffused TF. Active genesare marked as filled circles. The interactions between the genes areeither inhibitory (dashed arrows) or excitatory (solid arrows). In iii),two genes which form a negative feedback loop are highlighted, with anexcitatory interaction from the left to the right and an inhibitoryinteraction in the opposite direction. Each part i) to vi) of FIG. 3represents the state of the GRN in one time step. Note that the staticcondition for this individual is not yet reached after time step vi).

Evolutionary Algorithm

An evolutionary strategy ((μ,λ)-ES) with individual strategy parameteradaptation may be adopted. Details of the evolution strategy can befound, for example, in Hans-Paul Schwefel, “Evolution and OptimumSearch,” John Wiley, 1994, which is incorporated by reference herein inits entirety.

The main variation operator in the ES is the mutation operator that addsa normally distributed zero-mean random number to each object parameter.Each design variable has its own variance that self-adapts to thefitness landscape during evolution.

In contrast to conventional ESs, both gene transposition and geneduplication were implemented in the embodiments of the presentinvention. In one embodiment of the present invention, a transpositionis achieved in the following way: two randomly chosen units (both SUsand RUs are possible) are marked. Then, all units between these twomarked units are cut out and pasted to another randomly chosen position.Gene duplication is performed in a similar manner: only units betweenthe markers are copied and pasted to another randomly chosen position.Gene transposition and gene duplication are implemented at a certainprobability, which is denoted by pm·pt for transposition and pm·pd forduplication respectively where pd=1−pt.

FIG. 4 illustrates the best (dashed line) and average (solid line)fitness of a typical evolutionary run, according to one embodiment ofthe present invention. The shape of simple individuals, afterconvergence to a stable state, is shown illustratively for threedifferent generations.

Growth Processes for Optimization of Structured Materials

Structured materials are integrated systems that serve multiple roles,such as structural load bearing, thermal management, and energyabsorption. The structure materials exhibit a particular innerstructure, which is the main reason for their superior characteristicsover common materials.

Such inner structure can be described as specially shaped holes inside amaterial that are filled with another material/liquid/gas depending onthe intended use of the material. Examples include lightweight, loadbearing elements, thermal management and materials with integrateddamping.

Designing of such structured materials includes optimizing the innerstructure according to the needs and given constraints adapted for theirfunctions.

In one embodiment, a strategy is devised for designing the shape andmaterial properties used for the inner structure of functional materialsfor the uses mentioned above. Designing the number of holes along withthe shapes of holes is a high-dimensional mixed integer optimizationproblem where the quality function is given by nonlinear physicalproperties of the resulting design. Testing the real world designs isexpensive. Therefore a computational approach seems appropriate forparts of the developmental process. Construction of materials with voidsor other materials enclosed therein is a complex undertaking. A strategyto produce these structures needs to be included in the design process.

Evolutionary development of internal structured patterns may besimulated with cellular growth. Then, real-world bodies can be builtusing rapid prototyping or extrusion of 2D patterns.

EXAMPLES OF APPLICATION

Lightweight, yet stable structures: Voids inside a material can decreaseits weight and lower the material cost. To maintain a desired stabilityhowever, the number, position and shape of voids must be chosencarefully. The evolutionary developmental approach is capable of findingsuch configurations, optimizing number, position and shape of voids atthe same time. Such materials can find their application, for example,in aircrafts, automobiles, high-rise buildings, andmarine-constructions. Furthermore, self-similar patterns of voids andholes that go beyond simple repetitive periodic patterns can be producedusing the embodiments of the present invention.

Structures capable of heat transport: Heat transport in cooling devicesis usually achieved by conduction or convection. A heat exchanger isdesigned in a way that a solid body conducts heat from the heat sourceand transports it to an outer or inner surface (pipe like passages)where a stream of fluid (for example, air) removes the heat. The size,number and shape of both the outer and the inner surfaces can beoptimized such that a maximum heat transfer rate is achieved.

Lightweight structural elements with internal damping: Suppression ofoscillations caused by vibrations is a feature of modern materials thatis desirable in many industrial areas because oscillations can causematerial and joint fatigue as well as annoying auditory sounds.Inserting structured damping elements inside the material helps reducethese oscillations, reducing its effects while minimizing effects on thestability of the material.

Micro tubular structure of air diffusers/flow distributors: Inapplications where a flow field with specified characteristics is needed(for example, wind tunnels and chemical reactors), fluids are guided byair diffusers and flow distributors. The layout of such devices usuallyincludes tubes and nozzles that are optimized in its size, shape andnumber to produce the desired flow field.

Microscopic inner or surface structure of catalysts or membranes,supporting chemical reactions: In chemistry and biology, chemicalreaction is accelerated by means of a substance called catalyst. Boththe chemical characteristics of the material used as well as its surfacestructure may contribute to the improved performance of the catalyst.

The embodiments of the present invention may also be used forlab-on-a-chip and microfluidic devices such as micropump and microvalvedevices that require an internal microstructure to optimize suchcharacteristics as flow characteristics and fluid pockets.

While particular embodiments and applications of the present inventionhave been illustrated and described herein, it is to be understood thatthe invention is not limited to the precise construction and componentsdisclosed herein and that various modifications, changes, and variationsmay be made in the arrangement, operation, and details of the methodsand apparatuses of the present invention without departing from thespirit and scope of the invention as it is defined in the appendedclaims.

1. A method for optimizing an internal structure of a body, comprising:(a) encoding an initial phenotype design of the internal structure as aparameter set, the initial phenotype design of the internal structureencoded indirectly as a virtual genotype having parameters describingcell growth development of the phenotype using a gene regulatorynetwork; (b) processing the parameter set of the initial phenotypedesign by an evolutionary algorithm according to at least onepredetermined optimization criterion to generate an optimized parameterset, the processing of the parameter set terminated responsive to atermination condition of the evolutionary algorithm being met; and (c)outputting data representing the optimized parameter set.
 2. The methodof claim 1, further comprising: (d) building the body having theinternal structure according to the optimized parameter set.
 3. Themethod of claim 1, wherein the internal structure is a two dimensionalcross-sectional internal structure of the body or a three-dimensionalinternal structure of the body.
 4. The method of claim 1, wherein thestep (b) of processing the parameter set comprises: (e) producing one ormore offspring individuals of the virtual genotype; (f) developing cellgrowth of phenotypes of the offspring individuals by a gene regulatorynetwork until a development termination criterion is met; (g) computinga fitness value of the developed phenotypes; (h) selecting a virtualgenotype of the phenotype having best fitness value for producingoffspring individuals in step (e); and (i) repeating steps (e) to (h)until the termination condition of the evolutionary algorithm is met. 5.The method of claim 4, wherein the step (e) of producing the one or moreoffspring individuals comprises performing at least one of mutation,recombination, gene transposition, and gene duplication.
 6. The methodof claim 4, wherein the development termination criterion is met whenthe cell growth development reaches a predetermined number of discretesteps or a change in the cell growth development from a previous cycleis lower than a predetermined threshold.
 7. The method of claim 4,wherein cells represent presence of material or holes at a definedposition.
 8. The method of claim 7, wherein cells further representdifferent materials.
 9. The method of claim 4, wherein the phenotype ofthe internal structure is smoothened after the termination of the cellgrowth development and wherein outer cells represent control points of ahigher order spline surface.
 10. The method of claim 9, wherein materialboundary of a material of different type or holes is represented bypatches from a number of different spline surfaces.
 11. The method ofclaim 4, wherein cells move according to forces applied by other cellsor environment during the cell growth development.
 12. The method ofclaim 4, wherein cells interact physically in a form of a rigid bodyinteraction during the cell growth development.
 13. The method of claim4, wherein cells are pushed aside when a division occurs to reach a newstable arrangement during the cell growth development.
 14. The method ofclaim 1, wherein the number of parameters of the virtual genotype variesduring the step (b) of processing the parameter set.
 15. The method ofclaim 1, wherein the parameters of the virtual genotype define anactivity type and an action type of a cell during the cell growthdevelopment.
 16. The method of claim 15, wherein the activity type is atleast one of divide, die, release transcription factor, and produce acell adhering function.
 17. The method of claim 1, wherein theevolutionary algorithm comprises an Evolution Strategy.
 18. A computerprogram product comprising a computer readable storage medium structuredto store instructions executable by a processor in a computing deviceadapted to optimize an internal structure of a body, the instructions,when executed cause the processor to: (a) encode an initial phenotypedesign of the internal structure as a parameter set, the initialphenotype design of the internal structure encoded indirectly as avirtual genotype having parameters describing cell growth development ofthe phenotype using a gene regulatory network; (b) process the parameterset of the initial phenotype design by an evolutionary algorithmaccording to at least one predetermined optimization criterion togenerate an optimized parameter set, the processing of the parameter setterminated responsive to a termination condition of the evolutionaryalgorithm being met; and (c) output data representing the optimizedparameter set.